In computer graphics, calculating realistic shadowing and lighting terms for an arbitrary scene is a fundamental problem. When accurate interaction of lights with objects in a scene is achieved it greatly enhances the believability and the immersion that the viewer experiences. In this report we give a background to real-time shadow determination algorithms and present two approaches for real-time rendering of shadows that accurately model the umbrae and penumbrae of area light sources. A description of geometry shaders, a new technology in real-time rendering, is given, and we describe new methods that demonstrate how they can be used to shift significant amounts of mesh computation from the CPU to the GPU in the penumbra wedge soft shadow algorithm. We also present comparative and performance analyses of the soft shadow algorithms developed and discuss the performance characteristics of utilizing the geometry shader stage in shadowing algorithms. Our geometry shader based implementation provides a 21% performance increase to the penumbra wedge soft shadowing algorithm for certain meshes.